by which the distance between pairs of positions \(\textbf {r}_{k}(t),\textbf {r}_{l}(t),\)  or \(\textbf {r}_k(t),\textbf {r}_k(t+\delta t)\)  increases with
the Hubble velocity. Eq. (2) fulfills the Cosmological principle and the
Copernican principle for expansion of the universe [1]}. The Cosmological principle, which was first formulated by Newton [2]} demands,
that no place in the universe is preferred,
and the Copernican principle
demands, that no direction in the universe is preferred. Eq. 2 will accelerate the expansion of the universe, and
observations of galaxies indicates, that the distances between the galaxies accelerate (dark energy)[3]}, [4]}.
